document.write( "Question 123888: Ryan has 10-cent coins, 20-cent coins and 50-cent coins in his coin bank. 46 of them are not 20-cent coins, 54 of the coins are not 50-cent coins. The total number of 50-cent coins and 20-cent coins are 40. Find the total value of all the coins in his coin bank.\r
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Algebra.Com's Answer #90986 by ankor@dixie-net.com(22740)\"\" \"About 
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Ryan has 10-cent coins, 20-cent coins and 50-cent coins in his coin bank. 46 of them are not 20-cent coins, 54 of the coins are not 50-cent coins. The total number of 50-cent coins and 20-cent coins are 40. Find the total value of all the coins in his coin bank.
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\n" ); document.write( "Let x = 10-cent coins; Let y = 20-cent coins; Let z = 50-cent coins
\n" ); document.write( "Let t = total coins
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\n" ); document.write( "Ryan has 10-cent coins, 20-cent coins and 50-cent coins in his coin bank.
\n" ); document.write( "x + y + z = t
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\n" ); document.write( "46 of them are not 20-cent coins,
\n" ); document.write( "y = t - 46
\n" ); document.write( "y + 46 = t
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\n" ); document.write( "54 of the coins are not 50-cent coins.
\n" ); document.write( "z = t - 54
\n" ); document.write( "z + 54 = t
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\n" ); document.write( "The total number of 50-cent coins and 20-cent coins are 40.
\n" ); document.write( "y + z = 40
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\n" ); document.write( "Let's take the two equations that = t and make them = each other
\n" ); document.write( "y + 46 = z + 54
\n" ); document.write( "y - z = 54 - 46
\n" ); document.write( "y - z = 8
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\n" ); document.write( "pair this up with
\n" ); document.write( "y + z = 40
\n" ); document.write( "y - z = 8
\n" ); document.write( "-------------adding eliminates z
\n" ); document.write( "2y = 48
\n" ); document.write( "y = 24 ea 20-cent coins
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\n" ); document.write( "Find z using y + z = 40
\n" ); document.write( "24 + z = 40
\n" ); document.write( "z = 40 - 24
\n" ); document.write( "z = 16 ea 50-cent coins
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\n" ); document.write( "But what about x?
\n" ); document.write( "Substitute for y and z in the 1st equation
\n" ); document.write( "x + 24 + 16 = t
\n" ); document.write( "x + 40 = t
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\n" ); document.write( "We also know that z + 54 = t and z = 16; therefore t = 54 + 16 = 70
\n" ); document.write( "Using 70 for t:
\n" ); document.write( "x + 40 = 70
\n" ); document.write( "x = 70 - 40
\n" ); document.write( "x = 30 ea 10-cent coins
\n" ); document.write( ":
\n" ); document.write( "We have x = 30; y = 24; z = 16
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\n" ); document.write( "Find the total value of all the coins in his coin bank.
\n" ); document.write( "10(30) + 20(24) + 50(16) =
\n" ); document.write( "300 + 480 + 800 = 1580 cents; $15.80
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